Smooth kinetic maintenance of clusters

ABSTRACT

We propose a simple, deterministic kinetic data structure (KDS) for maintaining a covering of moving points by axis-aligned unit boxes in R^d. The number of boxes is always within a factor of 3^d of the best possible static covering. In the plane, this approximation factor (9) compares favorably with the approximation factor (around one million) of the best previous algorithm. The new KDS is efficient, local, compact, and responsive.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

General Terms:
Algorithms, Theory

Keywords:
clustering, kinetic data structures